Ellen Gallagher is about to have a one-person show at Tate Modern, AxME, followed six weeks later with one at the New Museum in New York City.

Gallagher's trajectory on to the international scene has been meteoric. She exhibited with the Gagosian Gallery shortly after finishing a residency in Provincetown, appearing in group shows such as Greater New York: New Art in New York Now at PS1 and the Whitney Biennial, with solo shows at Tate Liverpool and the Whitney, New York, along the way. Juliet Bingham, curator of the show at the Tate, says that Gallagher is "one of the foremost artists to have emerged from America in the 1990s.

AxME is Ellen Gallagher's first major retrospective in the UK and provides a timely moment to reassess works from many different periods". This is particularly notable as Gallagher is that unfashionable thing in the international art world: a woman and a painter. Having grown up in Providence, Rhode Island, the smallest state in the US and "all ocean", she is now based in Rotterdam, another city that straddles the sea, although she also maintains a studio in New York.

Born in 1965, Gallagher studied creative writing at Oberlin College before switching to art. After graduating from Boston's School of the Museum of Fine Arts, she attended Skowhegan School of Art before applying for the Provincetown residency programme. She admits that she was rejected the first year, but had encouragement from fellow African-American painter Alisha Henry to reapply. Gallagher has the last laugh here – the three paintings it turned down are in her Tate exhibition.

Provincetown was a place for her to focus on her work, and where "the water becomes a character in your life". Having stayed for an extra year, Gallagher admits that she knew it was time to get to New York, moving to Bushwick – she laughs, "I thought it was Williamsburg! That is what the real estate agent said." Gallagher recalls having orchids sent to her by Gagosian, not something that seemed appropriate to the area. "My work went off to have a fabulous life and I was living in Bushwick."

In Gallagher's studio, half-finished paintings rest on several easels near piled-up archival material – manipulated, covered in ink, cut up – the absent being as present as what is there. An unfinished canvas lined with handwriting paper, an ongoing technique, gives the surface a grid structure, showing Gallagher's allegiance to the "kinder" minimalism of Agnes Martin. Bingham says that "in her expanded painting practice, Gallagher questions what it is to be a modern subject, examining the centrality of race in the formation of the modern world, alongside simultaneous developments in modernist abstraction".

In the new canvases abstracted forms are in the process of being layered up with an accumulation of the manipulated archival material to be later carefully incised with a scalpel, carving the sharp edged almost sculptural forms. And like all of Gallagher's work there is the contradiction. "It is feminine but it is cut, it is so delicate but it is a scalpel. It is kind of butch and feminine."

Gallagher started using archival material, collaging it into her paintings in the early Nineties. She recalls discovering the African-American magazines Sepia, Ebony, Tan and Black Confessions in used-book shops on 42nd street when she visited New York from Provincetown. "I could go through a decade in an hour. I could disappear into these things." She was attracted by their ads, she says, mainly for wigs, hair-straightening aids and whitening potions, and the magazines' graphic quality. "One page would have been made of 20 ads. I could see a larger form in these smaller things."

Starting by drawing directly on to them, she started to cut into them with a scalpel, excising lips, eyes and specific letters, calling it her personal "scrimshaw". The text is not irrelevant, she says: "I cut out what I read. What slows it down is that improvisation, that riffing. What I read will affect what I make." She built up distinctive yellow wigs, which became as close to a signature work as she has made, culminating in the edition DeLuxe (2004) now in major museum collections around the world.

Much has been made of Gallagher's mixed parentage. Her father was a professional wrestler whose parents were from Cape Verde; her mother Irish. Gallagher points out that her mum brought her and her younger sister up as a single working mum, but also does not deny the palpable influence African-American culture has played on her work, although it is but one of many influences – musical, poetic, theatrical, scientific and maritime. The references that she scatters through our conversation, Pedro Bell, illustrator of Funkadelic, Sun Ra, jazz musician and composer, and writer Samuel Delany are all African-American artists.

Gallagher credits her mother with working hard to give her and her sister a good home, and she has imbued the artist with courage and resourcefulness as well. Gallagher has spoken about going to Alaska to work in the canneries with a friend and spending time on a scientific marine boat from Woods Hole, Massachusetts, and more prosaically about earning money at times by making croissants, sticky buns and working in restaurants.

Ultimately, though, as Gallagher says, "artists are self-generating. Regardless of your support you need to make work".

Gallagher shares her studio with her Dutch life partner Edgar Cleijne, whom she collaborates with on her films and other projects. She explains that this is part of the reason she is in Rotterdam, although "it could have been Amsterdam". She describes how she and Clejine were "hanging out" on Block Island in Rhode Island) and watching cormorants: "The cormorants were so comical. They had a distinct being to them."

It became the entry point for her film, also loosely inspired by another marine scientific discovery, the osedax, a tube-worm that feeds on the bodies of long-dead whales on the bottom of the sea. The technique of the film is, as in all of Gallagher's work, contradictory: effortless – a blob of ink serves as an entry point – and arduous and labour intensive. Glass slides on which she scratches, layers and works upon, sometimes get so thick with ink that they sometimes get spat out of the slide carousel as it turns.

This is not the first time the sea has inspired Gallagher's work. Earlier, she described walking by the sea and there being "a sense of things coming and going, being revealed". Murmur, drawings from the series Watery Ecstatic in 2005 was followed by Coral Cities, a group of works that pay homage to the African slaves who were thrown overboard and drowned, often for being nothing more than "sullen". It is only when peering closely at these seductively and beautifully rendered sea creatures, with their colourful tendrils, that the faces extracted from her archive appear, embedded, semi- revealed in the depths.

Gallagher is meticulous and hard working, making every mark, cut and incision herself. The residue is palpable, evidence of excised lips lie on the table near us. Gallagher says it is "like a mad hamster came thorough, there is a little trail like this, eyes, lips, the bottom of a hamster cage". It seems to me, it is a mark of respect to the archive, which she describes as "something of the past held hostage, and transformed into the future". I ask whether the process get easier, and my rather facile question is answered with her dazzling smile: "No, You would think after doing this for so many years it would get easier. But it doesn't! It hurts more."

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